Some time ago, in 2009 to be precise, a series of posts was made to the CLPEX.com chat board (a discussion group mainly for latent print examiners) that discussed intra-source versus inter-source variation.¹ I’ve replicated key parts of the discussion below, with quotes for the original posters, interspersing some of my own thoughts.

The discussion focused on latent print examination (LPE) but many of the concepts cross over to other disciplines, like handwriting examination.

Terminology is key to understanding so this discussion is worth a review.   

The original post was by L.J. Steele who asked,

Anyone have a good set of pictures to illustrate significant intra-source variation — two good-quality rolled prints or two latents known to be from the same person that might trip up a trainee (or even a veteran)? I’m looking for something for an article and/or powerpoint to help attorneys understand what I mean when I talk about intra-source explainable differences.

Then Pat A. Wertheim commented:

I don’t think I have ever heard the term “intra-source.” It is quite common to talk about “same source.” I am not even sure the meaning would be the same or whether there might be some fine distinction between the two.

Has anyone else ever used or heard the term “intra-source?” Is there any difference between that term and “same source?”

That’s where I’ll pick up the response provided by Glenn Langenburg:

(g.) Yeah in the community of folks looking at fingerprint statistics, these are commonly used terms.

I hold a much broader view on this as it applies far beyond the fingerprint realm. In reality, these terms are common to many applications and fields of study. The underlying concepts relating to the source(s) of variation are found throughout statistical theory and methods.

In fact, the differentiation of intra-source variation and inter-source variation is fundamental to most traditional parametric tests for statistical hypothesis testing; at least when it involves a comparison of means (i.e., t-test, ANOVA, etc.). For reference, I would say that the terms ‘intra-source’ and ‘inter-source’ are less often seen in the literature than the similar terms, ‘within-source’ and ‘between-source’. 

Glenn explains the terms as they pertain to the LPE realm, as follows: 

(g.) Intra-source variation is essentially represented by the concept of distortion (i.e. “how different can two impressions appear when in fact, they are from the same source skin”) versus Inter-source variation (i.e. “how similar can two impressions appear when in fact, they are from different sources)–what we might think of as close non-matches.

Given the nature of fingerprints, these fundamental concepts reduce to the points made by Glenn. However, in other domains such as handwriting comparison, the situation is a bit more complicated.  Nonetheless, exact parallels are present.²

The latter term sounds rather like a type of random match probability (RMP), doesn’t it?  What is the likelihood/probability that a set of common features would be observed, by chance alone, when the samples are in fact drawn from different sources taken from some (hopefully specified) population?  Without some estimation of the second factor (inter-source), how is it possible to determine the value of the first factor (intra-source)?  The short answer is, you can’t. 

Any given feature observed in a comparison will be ‘possible’ under either proposition; only the likelihood of observation changes.

(g.) In the statistical approaches proposed by Neumann, Champod, Mieuwly, Egli, and others, likelihood ratios represent these two competing parts: intra-source versus inter-source variations.  This is intuitive, since analysts are already doing this everytime we offer an opinion.  Everytime we report an identification, at some point we weighed the differences observed and asked ourselves, are these differences likely due to a distortion (within tolerance for Intra-source variation) or are they true discrepancies (within tolerance for Inter-source variation)?

As Glenn, notes this is all encapsulated perfectly in the concept of the likelihood-ratio used in the logical approach to evidence evaluation.

Ultimately, and in terms of the classical ‘identification’ opinion, this also means the examiner came to a conclusion that the evidence can only be explained in one way. All other possible explanations are deemed to be unreasonable to the point that they can be rejected outright. The main issue for most critics who disapprove of such opinions is the implicit application of some unknown threshold beyond which the expression of such a conclusion, an identification, can be justified. What is that threshold and how do we know it has been exceeded? Another obvious, and very important, issue is who should be making such decisions — the examiner or someone else? 

Any and all statistical methods, not just those of a ‘Bayesian’ nature, must take variation into account.³ Generally, this is done by contrasting and comparing within- and between- sources of variation. A simple truism that derives from these concepts is, as follows:

Differentiation between two potential sources can be achieved if and only if between-source variation exceeds within-source variation  

Basically, the spread between different (multiple) samples must exceed the spread for any given individual sample within the set of all possible samples. If there is too much overlap, the samples cannot be effectively distinguished from one another.

Glenn ended his comments with:

So you had experienced these concepts before, but maybe not heard these exact terms. Also, they differ from Intra-observer variation versus Inter-observer variation.  Whereas, the concept in the previous paragraph deals with how the features can present themselves in an impression (what arrangements are possible)…Inter/Intra observer variations deal with how analysts perceive features.  What features did I perceive today in an impression versus yesterday or last week (in the same impression) (INTRA-OBSERVER) v. How different are the observation from analyst to analyst all examining the same impression (INTER-OBSERVER).  I have some good data on this concept to share with the community soon (in the thesis).

I have to agree with Glenn on all his points.

The concepts of intra- versus inter- variation are both common to, and critical for, all forms of comparison (and, obviously) decision-making. This is a very interesting topic that comes into play for everything forensic examiners do on a regular basis — even though, as Glenn points out, the terms may not be particularly familiar to some people.